Extremal clique coverings of complementary graphs

D. de Caen, P. Erdős, N. J. Pullmann, N. C. Wormald

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let cc(G) (resp. cp(G)) be the least number of complete subgraphs needed to cover (resp. partition) the edges of a graph G. We present bounds on max {cc(G)+cc(Ḡ)}, max {cp(G)+cp(Ḡ)}, max {cc(G)cc(Ḡ)} and max {cp(G)cp(Ḡ)} where the maxima are taken over all graphs G on n vertices and Ḡ is the complement of G in K n . Several related open problems are also given.

Original languageEnglish
Pages (from-to)309-314
Number of pages6
JournalCombinatorica
Volume6
Issue number4
DOIs
Publication statusPublished - Dec 1986

Fingerprint

Clique
Covering
Graph in graph theory
Subgraph
Open Problems
Complement
Partition
Cover

Keywords

  • AMS subject classification (1980): 05C35

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)
  • Computational Mathematics

Cite this

de Caen, D., Erdős, P., Pullmann, N. J., & Wormald, N. C. (1986). Extremal clique coverings of complementary graphs. Combinatorica, 6(4), 309-314. https://doi.org/10.1007/BF02579256

Extremal clique coverings of complementary graphs. / de Caen, D.; Erdős, P.; Pullmann, N. J.; Wormald, N. C.

In: Combinatorica, Vol. 6, No. 4, 12.1986, p. 309-314.

Research output: Contribution to journalArticle

de Caen, D, Erdős, P, Pullmann, NJ & Wormald, NC 1986, 'Extremal clique coverings of complementary graphs', Combinatorica, vol. 6, no. 4, pp. 309-314. https://doi.org/10.1007/BF02579256
de Caen, D. ; Erdős, P. ; Pullmann, N. J. ; Wormald, N. C. / Extremal clique coverings of complementary graphs. In: Combinatorica. 1986 ; Vol. 6, No. 4. pp. 309-314.
@article{e5067357af2248b29cd28b27d64f7ad5,
title = "Extremal clique coverings of complementary graphs",
abstract = "Let cc(G) (resp. cp(G)) be the least number of complete subgraphs needed to cover (resp. partition) the edges of a graph G. We present bounds on max {cc(G)+cc(Ḡ)}, max {cp(G)+cp(Ḡ)}, max {cc(G)cc(Ḡ)} and max {cp(G)cp(Ḡ)} where the maxima are taken over all graphs G on n vertices and Ḡ is the complement of G in K n . Several related open problems are also given.",
keywords = "AMS subject classification (1980): 05C35",
author = "{de Caen}, D. and P. Erdős and Pullmann, {N. J.} and Wormald, {N. C.}",
year = "1986",
month = "12",
doi = "10.1007/BF02579256",
language = "English",
volume = "6",
pages = "309--314",
journal = "Combinatorica",
issn = "0209-9683",
publisher = "Janos Bolyai Mathematical Society",
number = "4",

}

TY - JOUR

T1 - Extremal clique coverings of complementary graphs

AU - de Caen, D.

AU - Erdős, P.

AU - Pullmann, N. J.

AU - Wormald, N. C.

PY - 1986/12

Y1 - 1986/12

N2 - Let cc(G) (resp. cp(G)) be the least number of complete subgraphs needed to cover (resp. partition) the edges of a graph G. We present bounds on max {cc(G)+cc(Ḡ)}, max {cp(G)+cp(Ḡ)}, max {cc(G)cc(Ḡ)} and max {cp(G)cp(Ḡ)} where the maxima are taken over all graphs G on n vertices and Ḡ is the complement of G in K n . Several related open problems are also given.

AB - Let cc(G) (resp. cp(G)) be the least number of complete subgraphs needed to cover (resp. partition) the edges of a graph G. We present bounds on max {cc(G)+cc(Ḡ)}, max {cp(G)+cp(Ḡ)}, max {cc(G)cc(Ḡ)} and max {cp(G)cp(Ḡ)} where the maxima are taken over all graphs G on n vertices and Ḡ is the complement of G in K n . Several related open problems are also given.

KW - AMS subject classification (1980): 05C35

UR - http://www.scopus.com/inward/record.url?scp=51649157071&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51649157071&partnerID=8YFLogxK

U2 - 10.1007/BF02579256

DO - 10.1007/BF02579256

M3 - Article

AN - SCOPUS:51649157071

VL - 6

SP - 309

EP - 314

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 4

ER -